Runge-Kutta methods for linear semi-explicit operator differential-algebraic equations

Altmann, R.; Zimmer, C.

doi:10.1090/mcom/3270

Runge-Kutta methods for linear semi-explicit operator differential-algebraic equations
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by R. Altmann and C. Zimmer PDF

Math. Comp. 87 (2018), 149-174 Request permission

Abstract:

As a first step towards time-stepping schemes for constrained PDE systems, this paper presents convergence results for the temporal discretization of operator DAEs. We consider linear, semi-explicit systems which include e.g. the Stokes equations or applications with boundary control. To guarantee unique approximations, we restrict the analysis to algebraically stable Runge-Kutta methods for which the stability functions satisfy $R(\infty )=0$. As expected from the theory of DAEs, the convergence properties of the single variables differ and depend strongly on the assumed smoothness of the data.

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